Overview

For each dam, we will:

  1. Assess concerns over data availability.
  2. Investigate multicollinearity between our three continuous covariates: flow, spill, and temperature.
  3. Look at passage timing, to determine when covariate data will be most useful.
  4. Decide how covariate data will be matched to state occupancy (e.g., a window approach)

Bonneville Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 302                   1                 148                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                  40                3205                3244

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -102.278  -23.211   -6.487   23.267  105.748 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -56.892413   1.137050  -50.03   <2e-16 ***
## flow          0.573623   0.005742   99.90   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 37.39 on 6447 degrees of freedom
##   (491 observations deleted due to missingness)
## Multiple R-squared:  0.6075, Adjusted R-squared:  0.6075 
## F-statistic:  9981 on 1 and 6447 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.832  -3.760   1.962   4.216   7.099 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 19.93859    0.23492   84.88   <2e-16 ***
## flow        -0.02268    0.00106  -21.39   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.164 on 3282 degrees of freedom
##   (3656 observations deleted due to missingness)
## Multiple R-squared:  0.1224, Adjusted R-squared:  0.1221 
## F-statistic: 457.7 on 1 and 3282 DF,  p-value: < 2.2e-16
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -88.661 -37.264   6.404  25.084 199.445 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  58.3157     2.7101  21.518   <2e-16 ***
## temp          1.4312     0.1667   8.585   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 52.3 on 3242 degrees of freedom
##   (3696 observations deleted due to missingness)
## Multiple R-squared:  0.02223,    Adjusted R-squared:  0.02193 
## F-statistic: 73.71 on 1 and 3242 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.142285 1.142285 
## 
## [[2]]
##     flow    spill 
## 2.092497 2.092497 
## 
## [[3]]
##    spill     temp 
## 1.022736 1.022736

John Day Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 300                   0                 279                   2 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                2072                 150                4137

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -84.785 -11.809   0.125  11.538  71.111 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -41.811462   0.647127  -64.61   <2e-16 ***
## flow          0.513038   0.003128  164.00   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 19.65 on 4285 degrees of freedom
##   (2653 observations deleted due to missingness)
## Multiple R-squared:  0.8626, Adjusted R-squared:  0.8625 
## F-statistic: 2.69e+04 on 1 and 4285 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.7495  -6.1562   0.4448   5.8534  10.4908 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 13.535326   0.183900  73.602  < 2e-16 ***
## flow        -0.005507   0.000962  -5.725 1.08e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.342 on 6207 degrees of freedom
##   (731 observations deleted due to missingness)
## Multiple R-squared:  0.005252,   Adjusted R-squared:  0.005092 
## F-statistic: 32.77 on 1 and 6207 DF,  p-value: 1.084e-08
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -90.67 -43.99   1.33  24.70 224.27 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   99.725      2.774   35.95   <2e-16 ***
## temp          -2.868      0.167  -17.18   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 51.23 on 4135 degrees of freedom
##   (2803 observations deleted due to missingness)
## Multiple R-squared:  0.06659,    Adjusted R-squared:  0.06636 
## F-statistic:   295 on 1 and 4135 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.191426 1.191426 
## 
## [[2]]
##     flow    spill 
## 7.179231 7.179231 
## 
## [[3]]
##    spill     temp 
## 1.071337 1.071337

The Dalles Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 280                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                 434                6591

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -101.903  -16.900    0.344   20.779  126.049 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -60.435506   0.778870  -77.59   <2e-16 ***
## flow          0.582702   0.004264  136.66   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27.74 on 7023 degrees of freedom
##   (280 observations deleted due to missingness)
## Multiple R-squared:  0.7267, Adjusted R-squared:  0.7267 
## F-statistic: 1.868e+04 on 1 and 7023 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.4977  -6.1205   0.3951   5.8010  10.4654 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 13.6825394  0.1810168  75.587  < 2e-16 ***
## flow        -0.0066120  0.0009764  -6.772 1.38e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.286 on 6589 degrees of freedom
##   (714 observations deleted due to missingness)
## Multiple R-squared:  0.006911,   Adjusted R-squared:  0.00676 
## F-statistic: 45.85 on 1 and 6589 DF,  p-value: 1.384e-11
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -62.61 -28.65 -17.73  21.11 272.82 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    7.596      1.421   5.347 9.26e-08 ***
## temp           2.441      0.101  24.168  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 51.71 on 6589 degrees of freedom
##   (714 observations deleted due to missingness)
## Multiple R-squared:  0.08143,    Adjusted R-squared:  0.08129 
## F-statistic: 584.1 on 1 and 6589 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.006959 1.006959 
## 
## [[2]]
##     flow    spill 
## 3.718405 3.718405 
## 
## [[3]]
##    spill     temp 
## 1.088647 1.088647

McNary Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 312                   0                   5                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                3336                   1                3286

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -108.245  -19.461    2.346   26.266   83.293 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -57.934979   1.547247  -37.44   <2e-16 ***
## flow          0.717774   0.006553  109.53   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 32.22 on 3285 degrees of freedom
##   (3653 observations deleted due to missingness)
## Multiple R-squared:  0.785,  Adjusted R-squared:  0.785 
## F-statistic: 1.2e+04 on 1 and 3285 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.2564  -6.0821  -0.0294   5.9025  17.1819 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.2039748  0.1781735  68.495   <2e-16 ***
## flow        -0.0014701  0.0009468  -1.553    0.121    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.227 on 6620 degrees of freedom
##   (318 observations deleted due to missingness)
## Multiple R-squared:  0.000364,   Adjusted R-squared:  0.000213 
## F-statistic: 2.411 on 1 and 6620 DF,  p-value: 0.1206
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -105.76  -42.26  -14.25   33.77  271.03 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  88.9768     3.2463  27.409  < 2e-16 ***
## temp          0.7798     0.2137   3.649 0.000267 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 69.36 on 3284 degrees of freedom
##   (3654 observations deleted due to missingness)
## Multiple R-squared:  0.004039,   Adjusted R-squared:  0.003736 
## F-statistic: 13.32 on 1 and 3284 DF,  p-value: 0.0002669

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.076439 1.076439 
## 
## [[2]]
##     flow    spill 
## 4.656695 4.656695 
## 
## [[3]]
##    spill     temp 
## 1.004056 1.004056

Priest Rapids Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 300                   0                 539                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   3                1754                 413                3931

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -66.503 -14.753  -0.855  12.376 104.397 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -43.643466   0.814950  -53.55   <2e-16 ***
## flow          0.604746   0.005838  103.58   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22.63 on 4342 degrees of freedom
##   (2596 observations deleted due to missingness)
## Multiple R-squared:  0.7119, Adjusted R-squared:  0.7118 
## F-statistic: 1.073e+04 on 1 and 4342 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.3340  -5.4218   0.4361   5.3795  16.2049 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.686109   0.188391  67.339  < 2e-16 ***
## flow        -0.009700   0.001424  -6.811 1.07e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.7 on 5683 degrees of freedom
##   (1255 observations deleted due to missingness)
## Multiple R-squared:  0.008097,   Adjusted R-squared:  0.007922 
## F-statistic: 46.39 on 1 and 5683 DF,  p-value: 1.07e-11
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -57.184 -25.880 -13.088   8.397 208.874 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   61.915      2.069   29.92   <2e-16 ***
## temp          -1.941      0.139  -13.96   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 41.82 on 3932 degrees of freedom
##   (3006 observations deleted due to missingness)
## Multiple R-squared:  0.04724,    Adjusted R-squared:  0.047 
## F-statistic:   195 on 1 and 3932 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.166272 1.166272 
## 
## [[2]]
##     flow    spill 
## 3.561882 3.561882 
## 
## [[3]]
##    spill     temp 
## 1.049833 1.049833

Rock Island Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 300                   0                1361                   4 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   1                2455                  51                2768

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -38.733 -10.232  -0.691   7.357 142.072 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -24.798526   0.931426  -26.62   <2e-16 ***
## flow          0.371051   0.006114   60.69   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.62 on 2817 degrees of freedom
##   (4121 observations deleted due to missingness)
## Multiple R-squared:  0.5667, Adjusted R-squared:  0.5665 
## F-statistic:  3684 on 1 and 2817 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.502  -5.198   1.156   5.159  10.797 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 14.358570   0.198881   72.20   <2e-16 ***
## flow        -0.019551   0.001536  -12.73   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.558 on 5221 degrees of freedom
##   (1717 observations deleted due to missingness)
## Multiple R-squared:  0.03009,    Adjusted R-squared:  0.02991 
## F-statistic:   162 on 1 and 5221 DF,  p-value: < 2.2e-16
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -30.059 -13.673  -5.187   4.154 202.394 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  26.3693     1.3765  19.157   <2e-16 ***
## temp          0.1881     0.1003   1.876   0.0608 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 25.31 on 2767 degrees of freedom
##   (4171 observations deleted due to missingness)
## Multiple R-squared:  0.00127,    Adjusted R-squared:  0.0009091 
## F-statistic: 3.519 on 1 and 2767 DF,  p-value: 0.06078

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.050743 1.050743 
## 
## [[2]]
##     flow    spill 
## 2.341262 2.341262 
## 
## [[3]]
##    spill     temp 
## 1.001268 1.001268

Rocky Reach Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 300                   0                1501                   4 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   1                2566                 140                2428

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -41.419 -11.545  -0.773   9.154 109.911 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -41.878738   0.929753  -45.04   <2e-16 ***
## flow          0.454827   0.006199   73.37   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.69 on 2566 degrees of freedom
##   (4372 observations deleted due to missingness)
## Multiple R-squared:  0.6772, Adjusted R-squared:  0.6771 
## F-statistic:  5383 on 1 and 2566 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.079  -5.248   1.198   5.199   8.633 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 14.066449   0.196478   71.59   <2e-16 ***
## flow        -0.017716   0.001556  -11.39   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.531 on 4992 degrees of freedom
##   (1946 observations deleted due to missingness)
## Multiple R-squared:  0.02532,    Adjusted R-squared:  0.02513 
## F-statistic: 129.7 on 1 and 4992 DF,  p-value: < 2.2e-16
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -31.206 -14.210  -9.083   1.796 183.579 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  32.7288     1.7305  18.912  < 2e-16 ***
## temp         -0.7408     0.1230  -6.024 1.96e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 29.64 on 2427 degrees of freedom
##   (4511 observations deleted due to missingness)
## Multiple R-squared:  0.01473,    Adjusted R-squared:  0.01433 
## F-statistic: 36.29 on 1 and 2427 DF,  p-value: 1.958e-09

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.065742 1.065742 
## 
## [[2]]
##     flow    spill 
## 3.139117 3.139117 
## 
## [[3]]
##    spill     temp 
## 1.014974 1.014974

Wells Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 300                   0                1614                   1 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   1                2004                 291                2729

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -31.795  -9.949  -1.668   6.978 186.266 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -36.226354   0.879033  -41.21   <2e-16 ***
## flow          0.402797   0.005993   67.21   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.21 on 3018 degrees of freedom
##   (3920 observations deleted due to missingness)
## Multiple R-squared:  0.5995, Adjusted R-squared:  0.5993 
## F-statistic:  4517 on 1 and 3018 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.696  -4.928   1.161   4.959  20.614 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 14.080640   0.193960   72.60   <2e-16 ***
## flow        -0.018928   0.001541  -12.28   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.419 on 4731 degrees of freedom
##   (2207 observations deleted due to missingness)
## Multiple R-squared:  0.0309, Adjusted R-squared:  0.0307 
## F-statistic: 150.9 on 1 and 4731 DF,  p-value: < 2.2e-16
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -24.819 -12.901  -9.831   0.778 164.143 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  26.0838     1.3793  18.911  < 2e-16 ***
## temp         -0.4459     0.1037  -4.301 1.76e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26.24 on 2728 degrees of freedom
##   (4210 observations deleted due to missingness)
## Multiple R-squared:  0.006736,   Adjusted R-squared:  0.006372 
## F-statistic:  18.5 on 1 and 2728 DF,  p-value: 1.759e-05

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##    flow    temp 
## 1.03328 1.03328 
## 
## [[2]]
##     flow    spill 
## 2.537075 2.537075 
## 
## [[3]]
##    spill     temp 
## 1.006809 1.006809

Ice Harbor Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 300                   0                   6                   1 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                3576                   1                3056

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -43.274  -8.645   3.409   8.920  33.472 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.74534    0.45081   -6.09 1.27e-09 ***
## flow         0.60800    0.00561  108.39  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.08 on 3055 degrees of freedom
##   (3883 observations deleted due to missingness)
## Multiple R-squared:  0.7936, Adjusted R-squared:  0.7936 
## F-statistic: 1.175e+04 on 1 and 3055 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.7475  -6.2896   0.3287   5.8157  10.6069 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.411765   0.126537  98.088  < 2e-16 ***
## flow        -0.008092   0.002161  -3.744 0.000183 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.394 on 6630 degrees of freedom
##   (308 observations deleted due to missingness)
## Multiple R-squared:  0.00211,    Adjusted R-squared:  0.00196 
## F-statistic: 14.02 on 1 and 6630 DF,  p-value: 0.0001825
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -62.835 -16.073  -4.107  13.741 103.354 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 67.41583    1.44656   46.60   <2e-16 ***
## temp        -1.89714    0.09043  -20.98   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26.9 on 3054 degrees of freedom
##   (3884 observations deleted due to missingness)
## Multiple R-squared:  0.126,  Adjusted R-squared:  0.1257 
## F-statistic: 440.1 on 1 and 3054 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.369567 1.369567 
## 
## [[2]]
##     flow    spill 
## 4.841629 4.841629 
## 
## [[3]]
##    spill     temp 
## 1.144117 1.144117

Lower Monumental Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 280                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                 461                6564

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -41.056  -4.884  -1.055   5.794  61.922 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -7.348479   0.201406  -36.49   <2e-16 ***
## flow         0.407361   0.003545  114.92   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.39 on 7023 degrees of freedom
##   (280 observations deleted due to missingness)
## Multiple R-squared:  0.6528, Adjusted R-squared:  0.6528 
## F-statistic: 1.321e+04 on 1 and 7023 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -11.493  -6.154   0.397   5.777   9.999 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.54669    0.12457 100.717  < 2e-16 ***
## flow        -0.01139    0.00214  -5.325 1.04e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.185 on 6562 degrees of freedom
##   (741 observations deleted due to missingness)
## Multiple R-squared:  0.004303,   Adjusted R-squared:  0.004151 
## F-statistic: 28.36 on 1 and 6562 DF,  p-value: 1.043e-07
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.928 -10.226  -7.655   3.084 126.833 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.07526    0.47818   12.71   <2e-16 ***
## temp         0.46397    0.03535   13.12   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.75 on 6562 degrees of freedom
##   (741 observations deleted due to missingness)
## Multiple R-squared:  0.02558,    Adjusted R-squared:  0.02543 
## F-statistic: 172.2 on 1 and 6562 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.004321 1.004321 
## 
## [[2]]
##     flow    spill 
## 2.870193 2.870193 
## 
## [[3]]
##    spill     temp 
## 1.026247 1.026247

Little Goose Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 280                   0                   0                   0 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                   0                 454                6571

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.082  -3.093   0.254   3.232 110.353 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -9.176430   0.180752  -50.77   <2e-16 ***
## flow         0.432874   0.003262  132.72   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.341 on 7023 degrees of freedom
##   (280 observations deleted due to missingness)
## Multiple R-squared:  0.7149, Adjusted R-squared:  0.7149 
## F-statistic: 1.761e+04 on 1 and 7023 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.0070  -6.0127   0.0896   5.9639  10.1816 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 12.041892   0.122645  98.185   <2e-16 ***
## flow        -0.005539   0.002158  -2.566   0.0103 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.102 on 6569 degrees of freedom
##   (734 observations deleted due to missingness)
## Multiple R-squared:  0.001002,   Adjusted R-squared:  0.0008496 
## F-statistic: 6.586 on 1 and 6569 DF,  p-value: 0.0103
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.849  -9.238  -7.103   2.647 172.191 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.75320    0.47600   12.09   <2e-16 ***
## temp         0.39236    0.03584   10.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.74 on 6569 degrees of freedom
##   (734 observations deleted due to missingness)
## Multiple R-squared:  0.01791,    Adjusted R-squared:  0.01776 
## F-statistic: 119.8 on 1 and 6569 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.001003 1.001003 
## 
## [[2]]
##     flow    spill 
## 3.504784 3.504784 
## 
## [[3]]
##    spill     temp 
## 1.018239 1.018239

Lower Granite Dam

Data availability

Availability of spill/temperature/flow data, by number of days (2004-present):

## 
##                none               spill                flow                temp 
##                 300                   0                   4                   2 
##        spill + temp         temp + flow        spill + flow spill + temp + flow 
##                   0                3746                   0                2888

Data by day of year

## [[1]]

## 
## [[2]]

## 
## [[3]]

Regressions and VIF

## [[1]]

## 
## [[2]]
## 
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.094  -6.462   0.713   5.075  55.431 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.422119   0.359471   1.174     0.24    
## flow        0.365865   0.004541  80.568   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.46 on 2886 degrees of freedom
##   (4052 observations deleted due to missingness)
## Multiple R-squared:  0.6922, Adjusted R-squared:  0.6921 
## F-statistic:  6491 on 1 and 2886 DF,  p-value: < 2.2e-16
## 
## 
## [[3]]

## 
## [[4]]
## 
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.9332 -5.8721 -0.3332  6.2410 10.3246 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.109e+01  1.179e-01  94.035   <2e-16 ***
## flow        6.304e-04  2.052e-03   0.307    0.759    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.914 on 6632 degrees of freedom
##   (306 observations deleted due to missingness)
## Multiple R-squared:  1.423e-05,  Adjusted R-squared:  -0.0001366 
## F-statistic: 0.09437 on 1 and 6632 DF,  p-value: 0.7587
## 
## 
## [[5]]

## 
## [[6]]
## 
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.474  -9.457  -2.193   2.938  97.860 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 43.40234    1.11588    38.9   <2e-16 ***
## temp        -1.29696    0.07412   -17.5   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17.93 on 2886 degrees of freedom
##   (4052 observations deleted due to missingness)
## Multiple R-squared:  0.09591,    Adjusted R-squared:  0.0956 
## F-statistic: 306.2 on 1 and 2886 DF,  p-value: < 2.2e-16

Variance inflation factors (Spill, Temperature, and Flow):

## [[1]]
##     flow     temp 
## 1.349425 1.349425 
## 
## [[2]]
##     flow    spill 
## 3.249202 3.249202 
## 
## [[3]]
##    spill     temp 
## 1.106086 1.106086